LOS b: Discuss the effective interest method and calculate interest expense, amortisation of bond discounts/premiums, and interest payments.

Interest expense is always equal to the book value of the bond at the beginning of the period multiplied by the market rate at issuance.

Step 1: Compute the present value of the bond: Since the current interest rate is above the coupon rate the bond will be issued at a discount.

FV = $5,000,000; N = 20; PMT = (0.04)(5 million) = $200,000; I/Y = 4.5; CPT → PV = -$4,674,802

Step 2: Compute the interest expense at the end of the first period.

= (0.045)(4,674,802) = $210,366

Step 3: Compute the interest expense at the end of the second period.

= (new balance sheet liability)(current interest rate)

= $4,674,802 + $10,366 = $4,685,168 new balance sheet liability

(0.045)(4,685,168) = $210,833

To determine the bond's market value one year from now: FV = 10,000,000; N = 4; I = 4; PMT = 450,000; CPT → PV = $10,181,495.

To determine the total interest expense:

1. FV = 10,000,000; N = 6; I = 4; PMT = 450,000; CPT → PV = $10,262,107. This is the price the purchaser of the bond will pay to the issuer of the bond. From the issuer's point of view this is the amount the issuer will receive from the bondholder.
2. Total interest expense over the life of the bond is equal to the difference between the amount paid by the issuer and the amount received from the bondholder.

[(6)(450,000) + 10,000,000] – 10,262,107 = 2,437,893

All of the cash flows for zero coupon bonds are included in cash flow from financing activities and none in cash flow from operations.

The interest paid on the bond will be the difference between the future value of the bond of $5,000,000 and the proceeds of the bond when it was originally issued.

First find the present value of the bond found by N = 8; FV = 5,000,000; I = 4; PMT = 0; CPT → PV = ?3,653,451.  This is the amount of money the bond generated when it was originally issued.

Then take the difference between the $5,000,000 future price and the $3,653,451 from the proceeds  = $1,346,549 which is the interest paid on the bond.

As bond premium is amortized, interest expense will be successively lower each period, thus increasing earnings over the life of the bond.

The value of the bond’s premium will be amortized toward zero over the life of the bond, not the value of the bond.

For the purpose of analysis, the value of debt should be adjusted for a change in interest rates. This will change the debt-to-equity ratio. Because changes in interest rates will change the market value of the debt, but not the coupon, interest expense will be unchanged. (However, if a firm has variable-rate debt, interest expense will change when interest rates change, but the market value of the variable-rate debt will not change significantly.)

First we must determine the present value of the bond. FV = 10,000,000; PMT = 560,000; I/Y = 6.5; N = 5; CPT → PV = 9,625,989, or approximately $9.626 million. At issuance, the university will receive cash flow from financing of $9.626 million.

• Interest expense in any given year is calculated by multiplying the market interest rate (at time of issuance) by the bond carrying value. For example, in year 1, interest expense = 9,625,989 × 0.065 = 625,689. Since the coupon payment = 10,000,000 × 0.056 = 560,000, the interest expense is “too high” by 65,689, and the carrying value of the bond is increased (through a decrease in the unamortized bond discount account) to $9,691,678. In year 2, using a similar calculation, the carrying value of the bond increases to $9,761,637. Thus, the interest expense in year 3 = 9,761,637 × 0.065 = 634,506, or approximately $0.635 million.

   

• Total interest expense is equal to the amount paid by the issuer less the amount received from the bondholder.

Amount paid by issuer = face value + total coupon payments
= 10,000,000 + (0.056 × 10,000,000 × 5) = 12,800,000
Total interest paid over the life = 12,800,000 – 9,625, 989 = 3,174,011, or approximately $3.2 million.

The coupon payment is a cash outflow from operations. ($10,000,000 × 0.09) = $900,000.

Newberg, upon issuance of the bonds, recorded bonds payable of (N = (2 × 7) = 14, PMT = $175,000, I/Y = (6/2) = 3, FV = $5,000,000) $5,282,402. Interest paid June 30, 2005, was ($5,282,402 × (0.06 / 2) =) $158,472. The coupon payment was $175,000, reducing bonds payable to ($5,282,402 – ($175,000 - $158,472) =) $5,265,874. Interest paid December 31, 2005, was ($5,265,874 × (0.06 / 2) =) $157,976. Total interest paid in 2005 was ($158,472 + $157,976 =) $316,448.

Beginning liability of the third period = liability of the second period + difference in the cash payment and the interest expense for the third period.

Liability for the first period = present value of the bond present value of the bond is computed as follows: FV = 1000 PMT = [(1000)(0.08)]/2 = 40 I/Y = 5 N = 10 Compute PV = -923

Liability for the second period = 923 + [(0.05)(923) – 40] = 923 + 6 = 929

Liability for the third period = 929 + [(0.05)(929) – 40] = 929 + 6 = 935

The bonds issued at premium will have the highest cash flows from financing.

The zero-coupon bond will have higher cash flows from operations, as the cash interest expense in this case is zero and no cash is paid until maturity. Candidates should remember that any bond issued at a discount will have more cash flow from operations and less cash flow from financing.

Upon issuance, cash flow from financing will be increased by the amount of the proceeds.

Under the effective interest rate method, the bond liability is equal to the present value of the remaining cash flows discounted at the market rate of interest at the issue date. At the end of this year, there are 3 annual payments of $600,000 and one payment of $10,000,000 remaining. Using your financial calculator, the present value is $9,737,568 (N = 3, I = 7, PMT = 600,000, FV = 10,000,000, Solve for PV).